A note on recent criticisms to Birnbaum's theorem

TL;DR

This paper defends Birnbaum's theorem against recent criticisms, affirming its validity and ongoing relevance in statistical theory.

Contribution

It offers a critical commentary reaffirming the correctness of Birnbaum's theorem and addresses recent doubts raised by Evans and Mayo.

Findings

Birnbaum's theorem remains valid.

Criticisms by Evans and Mayo are addressed and refuted.

The implications of Birnbaum's theorem are still relevant.

Abstract

In this note, we provide critical commentary on two articles that cast doubt on the validity and implications of Birnbaum's theorem: Evans (2013) and Mayo (2014). In our view, the proof is correct and the consequences of the theorem are alive and well.